The announcement comes after up to 12 Israeli air strikes over Gaza City on Saturday and Sunday left at least two people dead and up to 25 others injured, including children.
"I have issued orders that there be no restrictions regarding the use of all means to strike at the terrorists, members of terrorist organisations, and their equipment and their hideouts," Sharon told cabinet ministers.
"We don't intend here to stage a one-time action, but intend to carry out a continued action, whose aim is to hurt the terrorists and not to let up," he said.
"We should use every means at our disposal to stop this phenomenon."
The strikes began on Saturday afternoon and continued into the early hours of Sunday, which the Israeli army described as a "prolonged" operation against Hamas.
Hamas and other Palestinian resistance groups had fired about 30 Qassam rockets at Israeli towns in retaliation for a deadly explosion at a Gaza rally on Friday which it blamed on Israel.
That explosion killed at least 17 people, including several civilians, and injured scores of others.Women, children injured
The firing of the Qassam rockets, which lightly wounded six Israelis, was the first attack mounted by the group since the Gaza pullout.
Also on Sunday, Israeli warplanes stuck a school in crowded Gaza City, injuring 15 poeple, many of them children.
A 40-day-old baby is among the
Palestinians injured in the attack
The blast struck the al-Arkam school, established by the late founder of Hamas, Shaikh Ahmad Yassin, which is situated in the Tufah neighbourhood - a densely populated area and a Hamas stronghold.
The blast collapsed part of the school and caused damage to at least five nearby homes.
Hospital officials said women and children were among the wounded, and one person was in serious condition.
Hopsital sources said a 40-day-old baby was among the injured.
Electricity in the neighbourhood was cut, and dozens of people ran into the streets after the attack.
Soon after, in another strike, Israeli helicopters fired three missiles in the northern Gaza Strip.
The Israeli warplanes also struck
the Jabalya refugee camp
The army targeted foundries and metal workshops.
Israel, however, said the targets were a weapons-storage facility in the Jabalya refugee camp used by the Popular Resistance Committees.
These claims were denied by the buildings' proprietors, Aljazeera's correspondent said.
A building in Bait Hanun housing the offices of the Popular Front for the Liberation of Palestine (PFLP) was also attacked.
Residents in Bait Hanun said the PFLP building suffered heavy damage, but said no one was believed to be inside at the time.
Earlier on Sunday, a senior Israeli commander hinted that Hamas leaders could be targeted.
Major-General Yisrael Ziv, the army's head of operations, said "it was decided to launch a prolonged and constant attack on the Hamas" and the attacks would target "all faces" of Hamas.
Sharon has approved a series
of military raids into Gaza
Asked whether the lives of Hamas' leaders were in danger, he said: "Let them decide for themselves."
Israel killed dozens of Hamas members during four years of fighting, but had halted the practice since a February ceasefire declaration. Arrests
Israeli security officials said that "Operation First Rain" would include artillery fire, air strikes and other targeted attacks.
The officials said the operation would intensify, leading up to a ground operation unless the Palestinian security took action to halt the rocket attacks, or Hamas ended the attacks itself.
They also said Israel's closure of all Palestinian areas, imposed on Saturday, would continue.
The small number of labourers usually given permission to work in Israel also would not be allowed through Gaza border crossings and West Bank checkpoints.
Palestinian President Mahmoud Abbas said on Sunday the latest Israeli air strikes and mass arrest operations in the West Bank were without justification.
"We regret this aggression and I believe that there can be no justification for these operations," Abbas said.
The president will meet Egyptian President Hosni Mubarak in Cairo on Tuesday to discuss the deteriorating security situation in the Gaza Strip, Aljazeera's correspondent in Palestine quoted a Palestinian source as saying.
The meeting will also tackle Israeli threats and the issue of reopening the Rafah border crossing, the correspondent added.
Meanwhile, on Sunday, the Israeli army carried out a massive sweep of arrests, targeting Hamas activists and political leaders throughout the West Bank.
Hamas election candidates have
been detained by Israeli forces
Palestinian sources reported the arrests of as many as 230 activists including teachers, students, doctors, journalists and professionals in the regions of Hebron, Bethlehem, Ram Allah, Nablus and Tulkarim.
Hamas chief spokesman in the West Bank, Hasan Yusuf, was among the detainees, sources say.
It was not clear if the latest arrests are intended to prevent Hamas from taking part in the January elections of the Palestinian legislative council.
Many of the detainees are believed to be actual or potential candidates for the upcoming elections.
Khalid Amayreh in the West Bank contributed to this report